But none of the data suggest growth is robust enough to pressure central banks on either side of the Atlantic to tinker with highly stimulative monetary policies.

The Institute for Supply Management said on Friday that its purchasing managers’ index (PMI) for US service firms grew at its fastest pace in 10 months in December, boosted by a rise in new orders. The pace of hiring in the sector hit a five-month high.

Throughout the US economy, employers added 155 000 new workers last month, a separate report on Friday showed. Gains were distributed broadly, which economists say suggests that the economy will probably grow by about 2 percent this year.

The 17-country euro zone, on the other hand, probably closed the year in recession, though evidence that the pace of contraction in the service sector had slowed suggested things may be turning around.

“I think [the euro zone PMIs] are showing a decisive bottoming-out of activity,” said James Nixon, the chief European economist at Société Générale. “Now, the actual levels of the surveys are still consistent with gross domestic product declining, but at least things aren’t getting worse any faster.”

According to financial information firm Markit, the euro zone’s composite PMI, which measures the activity of thousands of companies, rose to 47.2 last month, its highest since March.

The decline eased among firms such as banks and restaurants although things looked worse for manufacturers.

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The surveys at least bring some substance to the belief that the worst is over and that a return to growth is in sight for the region in 2013,” said Chris Williamson, the chief economist at Markit.

The UK services PMI, however, slipped to 48.9 from 50.2, sagging below the 50 point mark that divides expansion and contraction for the first time in two years.

Survey compiler Markit said the figures suggested that Britain’s economy shrank 0.2 percent in the final quarter of 2012, a slightly bigger drop than most other private sector forecasts.

Friday’s European data followed news that China’s services sector saw its slowest rate of expansion in nearly 18 months in December, although the HSBC services PMI still pointed to a modest revival.

With Europe likely to remain in recession, the world economy will increasingly depend on China and the US to provide the fuel for growth.

Recent US data, particularly from the labour market, has been encouraging, not least because firms continued to hire in December despite a looming government budget crisis that many feared would bring recession this year if not solved.

The US Congress struck a deal to avoid going over the so-called fiscal cliff of tax hikes and spending cuts on New Year’s Day, though decisions on important spending issues were delayed.

Bond markets also got a scare on Thursday as minutes revealed that some Federal Reserve officials thought it appropriate to wind down the central bank’s open-ended asset purchase programme, known as quantitative easing, before the end of 2013. That prompted a spike in long-dated bond yields, though Friday’s data showing the US jobless rate rising to 7.8 percent eased some of those fears.

Economists think the European Central Bank may cut interest rates after holding them at a record low 0.75 percent last month. – Steven Johnson and Andy Bruce New York and London from Reuters